1. Capital Structure Modigliani-Miller
Finance - Pedro Barroso

2. Capital Structure and the Pie
Market value of a firm is the sum of the value of the firm’s debt and the firm’s equity: V = D + E
Goal of the firm’s management is to make the firm as valuable as possible, then the firm should pick the debt-to-equity ratio that makes the pie as big as possible S D E
Value of the Firm
Finance - Pedro Barroso

3. Stockholder Interests
There are two important questions:
Why should the stockholders care about maximizing firm value? Perhaps they should be interested in strategies that maximize shareholder value.
What is the ratio of debt-to-equity that maximizes the shareholder’s value?
As it turns out, changes in capital structure benefit the stockholders if and only if the value of the firm increases.
Finance - Pedro Barroso

4. Variety of Capital Structures Out There
AT&T Boeing Boston Edison John Deere Delta Air Lines Disney General Motors Hewlett-Packard McDonalds 3M Philip Morris Raytheon Safeway Stores Texaco Wal-Mart
Company Name
Debt
Debt + Mkt Equity
Total Book Assets
EBITDA
Interest
20%
29%
Finance - Pedro Barroso

5. Modigliani-Miller Assumptions
Perfect capital markets:
no transaction costs and no taxes
no bankruptcy costs
no agency costs
no asymmetric information in capital markets
no arbitrage
Finance - Pedro Barroso

6. MM Proposition I (No Taxes)
Total market value of the firm (debt + equity) is not affected by the capital structure
“The size of the pie does not change no matter how you slice it”
A firm’s value is determined by its real assets and growth opportunities, not by the types of securities it issues
Cost of capital is independent of capital structure
Finance - Pedro Barroso

7. MM Proposition I (No Taxes)
We can create a levered or unlevered position by adjusting the trading in our own account
This homemade leverage suggests that capital structure is irrelevant in determining the market value of the firm:
VL = VU
Finance - Pedro Barroso

8. Home-Made (Un)Leverage
Consider twin firms with same assets that generate perpetual cash flow FCF
Notice that FCF = EBIT (= 100)
No taxes
Zero growth: Depreciation = CAPEX, Working capital = 0
Unlevered firm U: all-equity firm with value VU = E (= 1500)
VU = EBIT / rU , rU is cost of capital of unlevered firm
Levered firm L: firm with debt and equity; firm value VL = D + E (= = 1500)
Debt is perpetual bond with coupon of DrD (rD = 10%)
Finance - Pedro Barroso

9. Home-Made (Un)Leverage
Strategy A: investor buys 10% of levered firm (L) equity, which is 10%E
Cost = 10%(VL-D)
Strategy B: investor buys 10% of unlevered firm (U) with loan of 10%D at interest rate of rD plus own investment of 10%(VU – D)
Cost= 10%(VU – D)
Finance - Pedro Barroso

10. Home-Made (Un)Leverage
Strategy A payoff: 10%[EBIT – DrD]
10% [100 – 500 x 10%] = 5
Strategy B payoff:
10%EBIT – 10%DrD = 10% [EBIT – DrD]
10% x 100 – 10% x 500 x 10% = 5
Finance - Pedro Barroso

11. Home-Made (Un)Leverage
No arbitrage condition: investments with equal payoffs must have same initial investment
10% (VL-D) = 10%(VU – D) [10% x 1000 = 10% ( )]
VU = D + E
VU = VL
Investors can leverage (or unleverage) a firm’s capital structure to any given level through a personal loan (or deposit)
Finance - Pedro Barroso

12. MM Proposition II (No Taxes)
where:
rU is cost of capital of unlevered firm (all-equity)
rE is cost of equity (or required return on equity)
rD is cost of debt
E is market value of equity
D is market value of debt
WACC is weighted-average cost of capital
Finance - Pedro Barroso

13. MM Proposition II (No Taxes)
Define the weighted average cost of capital:
Set rU = WACC (cost of capital is independent of capital structure)
Finance - Pedro Barroso

14. MM Proposition II (No Taxes)
Cost of capital rU rD rD
Debt-to-equity ratio
Finance - Pedro Barroso

15. Finance - Pedro Barroso
MM II (No Taxes)
Increasing the debt load does not affect the riskiness of the assets, but it does increase the riskiness of the equity
In the same firm, rD is always less than rE, because the debt has a higher priority and thus less risk
But the weighted sum (WACC) of the costs of debt and equity is always a constant
Finance - Pedro Barroso

16. MM (With Corporate Taxes)
Corporate taxes on profits introduce a new claimholder on the firm’s cash flows (government)
Maximum corporate tax rate in the US is 34% and 25% in Portugal
Minimizing government’s share of the pie leaves more for debt and equity holders
Financing policy can be a tool to increase firm value (i.e. market value of debt plus market value of equity)
Finance - Pedro Barroso

17. MM (With Corporate Taxes)
A firm has pre-tax cash flow FCF = EBIT and interest payments D rD
Firm pays corporate tax at rate t
After-tax cash flow to shareholders and debtholders: FCF = EBIT (1 – t) + t D rD
NI + D rD = (EBIT – D rD ) (1 – t) + D rD
t D rD is tax shield from debt (interest tax shield)
Levered firm value is present value of FCFs
Finance - Pedro Barroso

18. Finance - Pedro Barroso
Example
Unlevered Firm
Levered Firm
EBIT
100
Interest expenses (rD x D)
10 = 10% x 100
Earnings before taxes 90
Taxes (t = 30%) 30 27
Net Income 70 63
FCF (NI + Interest expenses)
73 =
Finance - Pedro Barroso

19. MM Propositions I & II (With Taxes)
Proposition I: Firm value increases with leverage
VL = VU + tD
Proposition II: Some of the increase in equity risk and return is offset by the interest tax shield
Optimal capital sructure: 100% debt!
Finance - Pedro Barroso

20. MM Proposition II (With Taxes)
Expected cash flow from LHS of balance sheet can be written as:
Expected cash flow to debtholders and stockholders can be written as:
Thus,
Finance - Pedro Barroso

21. Finance - Pedro Barroso
WACC (With Taxes)
Weighted average cost of capital (WACC) with corporate taxes:
Thus,
Finance - Pedro Barroso

22. MM Proposition II (With Taxes)
Cost of capital rU rD
Debt-to-equity ratio (D/E)
Finance - Pedro Barroso

23. Total Cash Flow to Investors
All-equity firm Levered firm E G E G D
Levered firm pays less in taxes than does the all-equity firm
Thus, the sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm
This is how cutting the pie differently can make the pie “larger” - the government takes a smaller slice of the pie!
Finance - Pedro Barroso

24. Finance - Pedro Barroso
Caveats
Correct tax rate to value the interest tax shield is the expected marginal tax rate, or the expected increase in the firm’s tax liability when its taxable income increases by $1. This may not be the statutory rate!
The firm may not always be taxable
Earnings may not be large enough to fully utilize the shield
Tax losses can be carried back 2 years or forward 20 years in the U.S.; only carry forward 4 years in Portugal
Non-debt tax shields may already suffice to offset earnings
Depreciation
Investment tax credit
Finance - Pedro Barroso